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a(n) is the maximum number m such that m white kings and m black kings can coexist on an n+1 X n+1 chessboard without attacking each other. - _Aaron Khan_, Jul 05 2022
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This sequence is also the Peaceable Kings sequence (as per A250000 Peaceable Queens, but using kings instead of queens), the only difference being that Peaceable Kings sequence would begin with an additional 0. I.e. a(n) is the number of opposing kings that can fit on an n+1 X n+1 size chessboard such that no kings of opposite colours are attacking each other.
a(n) is the maximum number m such that m white kings and m black kings can coexist on an n+1 X n+1 chessboard without attacking each other.
Examples of the sequence when used for Peaceable Kingskings on a chessboard:
(MAGMAMagma) [(n^2-3*n+1+(-1)^n)/2: n in [3..100]]; // Vincenzo Librandi, Mar 24 2011
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This sequence is also the Peaceable Kings sequence (as per A250000 Peaceable Queens, but using kings instead of queens), the only difference being that Peaceable Kings sequence would begin with an additional 0. I.e. a(n) is the number of opposing kings that can fit on an n+1 X n+1 size chessboard such that no kings of opposite colours are attacking each other.
.
Examples of the sequence when used for Peaceable Kings:
.
A solution illustrating a(2)=3:
+-------+
| B B B |
| . . . |
| W W W |
+-------+
.
A solution illustrating a(3)=5:
+---------+
| B B B B |
| B . . . |
| . . . W |
| W W W W |
+---------+
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11000...01
11100....0
01110.....
00111.....
..........
..........
00.....111
10.....011
P. Paul Barry, <a href="http://arxiv.org/abs/1205.2565">On sequences with {-1, 0, 1} Hankel transforms</a>, arXiv preprint arXiv:1205.2565 [math.CO], 2012.
11001
11100
01110
00111
10011
10001
01100
01100
00011
10010
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